 And thank you for sacrificing your day and being with us today. We're going to start in two minutes. Please also remember to complete the register. I've just posted the link on the chat so that you can complete that while we wait. We wait for that two minutes. Okay, so we can start with today's session. Today we're going to look at simple interest and discount interest and simple discount. As part of our session for today. And the following week we're going to look at the compound interest and the other week we're going to look at annuities. So brace yourself for a long engaging session because I just have about two or three slides where we... I do give an example and then the rest of the slides is you doing the activities and then we feedback. Remember we follow Newman's error prompt. Understand what you are given in the question. Identify all the facts. Identify the formula that you would need to use and then do the calculations afterwards. So let's start. But before we start, do you have any questions? Do you recommend anything you want to say to me before we start with today's session? Nothing? Okay, in the absence of questions, then we can continue with today's session. Like I said, we're going to do simple interest. I hope you have with you your calculators and you are ready to do some calculations. I'm going to share with you some formulas that we're going to be using and you just need to make sure that you have those formulas next to you as we continue. I'm not sure if any comments in the chat or anything like that. Okay, so nothing. Okay, so let's start with today's session. So by the end of the session today, you should at least know how to do some basic calculation when it comes to questions relating to simple interest or simple discount. What is a simple interest? Simple interest is the amount you pay when you go borrow money or the amount you will receive when you save money. That is simple interest. It's just the amount you will receive if then. It's not a rate. It's an amount. The sum of money that you will receive either when you pay a loan back, you pay loan with interest. And that is the amount of interest. That is what we're looking for. And when you save money, you save money so that at the end your money can be accumulated. And when it's accumulated, your principal amount, which is the amount that you saved from the origin plus the interest makes up your accumulated amount. And if we just want to know how much interest you would have received, you just need to subtract your principal amount from the accumulated amount so that you can see how much interest you have received or you have paid. That is as easy as it is with simple interest. And interest is calculated as a fraction of the amount you borrow or you have saved in terms of the principal amount in that time period as well. So when you calculate simple interest, because it's a fraction of the amount you would have received or you would receive when you borrow money or you will pay back when you borrow money or you will receive when you have saved money. And simple interest is only payable at the beginning of the term so it means they can calculate your simple interest and say this is how much your interest is and then you pay it at the beginning. So it's included at the beginning of the term when you start with the saving or when you start borrowing the money. So in order for us to calculate the simple interest we use the formula, interest is equals to the principal amount times the rate times the period, which is the time and our time here will always be in years. Therefore it means our interest rate will be per year, will also be per year. Your present value or your principal amount is the amount at the beginning, the amount excluding interest and your I is your interest amount. So how do we then calculate this? If for example I want to calculate the future which is the accumulated amount, then my accumulated amount will be, which is my future amount will be your principal value plus your interest. And in terms of your interest we know that we have calculated that we said our interest is I and I we can calculate it as PRT and our future value can be your principal amount plus your interest. And because we're using mathematical formulas and that formula will look like this. We take out P as a common factor and we end up having one plus RT times P. So our accumulated amount or our future value amount we always going to use the formula. S is equals to PRT. When we calculate our interest we just going to use this formula. We can use them interchangeably when we are asked to calculate the interest amount or we are asked to calculate the present value and we are given the interest amount and you are given the rate and we are given the period how long. You can calculate P or you can calculate R or you can calculate T based on this by changing the subject of the formula and remember we did cover some of those concepts changing the subject of the formula. So for example if they give you the future value the present value and they ask you to calculate the rate which is the interest rate and simple interest rate then you need to be calculating R. So then you need to make R the subject of the formula and by now you would know how to do that. The other thing for simple interest discount interest we going to use formulas only if you have a financial calculator the only time we will use the financial calculator functions when it comes to the amortization payment and all that and cumulative amount and future values and present value. Those we going to start when we talk about compounding periods. With simple interest and simple discount we always use formulas so you must always remember that if in your question it asks you or they tell you that simple discount is you must know that you are going to use a formula. If they tell you simple interest is then you know that you can use a formula to calculate that but if they say compounded and you have a financial calculator then you can use your financial calculator to do the compounded accumulated amount and so forth. Now let's look at examples. You borrow an amount of 7500 at an interest rate of 15% per annum or per year. What will you pay or what will you have to pay back if you repay the loan within four months. Remember when I explained that the period T is always in years so it means if you are giving months like here you are giving months you need to convert your months into a year therefore it means you will divide your months by 12 months to convert that into a year. So the formula we can identify but before we identify the formula we need to identify what we are given and what are we asked in this question so we are asked that what will you have to pay back if you repay the loan within four months. So yeah they are asking us to pay to calculate the future value which is our S. Therefore it means if I go back to our statement you borrow an amount of 7000 so I'm borrowing therefore this is my present value at an interest rate and this because I know that I am busy with simple interest but usually they will say yeah at a simple interest rate. So I know that that is my simple interest rate and therefore that is my R. Now the other thing that you need to take into consideration unless you know how to use your calculator with the percentage your R you need to divide 15% by 100. So therefore it will be 0,15 because 15 divided by 100 so this is the same as 15 divided by 100 will give you 0,15. When we work in financial meds as well what you need to remember as well is that when we calculate the rate you do not round it off. So 15 will stay as 0,15 if it was 15,5 the rate would have been 0,155 it doesn't really matter you need to keep all the decimal. If it was 15,54 you will leave the answer as 0,1554 like that you do not round it off you keep all the decimals just remember that. Okay so what else are we given? We are told it's per annum and we need to pay back so the future value and we need to pay it back within the four months and that is our T but we know that we need to convert this to a year. So therefore it means we're going to say 4 divided by 12 and that will give us the T in years or our term in years. So now I have identified everything that I need only what is left is I need to find the formula. I identify the formula that we will use to calculate this and now I can substitute into that formula and start calculating. Our S is what we are looking for P is 7,500 times 1 plus our rate of 0,15 times our T which is 4 divided by 12 and when you solve the entire equation or we can do step by step so it will be. So if you have a cashier calculator you can put this whole thing in a calculator but because I'm calculating manually so 4 divided by 12 multiplied by 0,15 it gives me 0,05 plus 1 will give me 1,05 times 7,500. And the answer that I will get will be the accumulated amount or the money that I will have to pay repay back for the loan within four months will be 7,875 and that's how easy it is to calculate the future value of a simple interest. Any questions before I move on to the next part of the session? No questions. So how do we then calculate a discount? So a simple discount is a process of finding the present value of a given amount that is due on a future date and it includes simple interest. So in other words, to discount an amount by a simple interest process is to find its present value. The difference between the amount and its present value is called the discount or the simple discount. And that is always the discount is always given or the discounted value is given by your principal amount times the discounted rate times the period. The discounted rate will be the rate given to you in years as well. And the period always remember that we always calculate it in years. And you do here on my slides, I've got this wrong. This is not a simple interest but a simple discount discount rate. That is a simple. No, no, no, that is not a simple discount rate that is. Gosh, I'm doing all wrong. This is the discounted value. Discounted. Discounted value. Sorry, my bad. The small D is your discount and your simple discount rate. Okay, so let's then look at this. So your discounted value usually is the same as your principal amount minus your discount. And remember your discount will be that. So if we need to calculate the actual discounted value, then we need to take our principal amount and subtract the discount value that we have. Then we will know how much what is the discounted value. Actually, we can go back there because I called that one a discounted value, which is just a discount. So this is just a D. This is just a discount that you will have. It's not a discounted value, but your discounted value will be your principal minus the discount amount. So if we want to calculate the discounted value as well, we can use the same formula in state of using our S is equals to P times one plus RT. We're going to subtract that part, so it will be one minus DT as well. So let's look at an example. I will apply this knowledge. Anna borrows 1200 for 10 months at a discount rate of 15% per annum. Determine the discount and the discounted principal. So what they're asking us, there are two things here. We need to determine the discount, which is the capital letter D. And also from there, we need to determine the discounted principal. So the discount, before we go to the discount, so we can identify the formula, but what else are we? We already established that we need to calculate the discount, and we also need to calculate the discounted amount, which is that. What are we given? Anna borrows 1200 because they are borrowing that is our present value for 10 months. 10 months is our time, which we can divide 10 divided by 12 at a discount rate, which is then our D of 0,15. And then we can substitute into the formula. So we know that our P is 1200, our D is 0,15, and our T is 10 over 12, and our discount is 150. We can use either of the formulas. We can use this formula or that formula to calculate the discounted principal. So we'll use the second, the last one. The discounted principal, it's P times 1 minus D times T close bracket. Our P is 1200 minus D, which is 0,15 and T, which is 10 over 12. And that gives us 1050. If we use the first one, which states clearly P minus D, we already calculated D, we know what P is. So 1200 minus 150 will give us the same amount, it's 1050. So you can use either of the formula to calculate the discounted formula or the discounted value. And that is simple interest and simple discount. Let's do some exercises. Since it's still the beginning, I'm going to give you some hints in terms of formulas, but going forward, you will have to go and identify the formulas yourselves. Okay, so question number one or exercise number one, which we can do together as well, because we're still learning some of this concept now. Joseph invests 36,000 at a simple interest of 6% per annum. How long will it take for Joseph's investment to grow to 55,400 and 40? So the question, what does the question say? The question asks us to find out how long therefore it means we need to find T. So what are we given? They invest 36,000, so that is our P. And a simple interest that is good because then it tells us that the formula that we're going to be using is that formula. S is equals to P times 1 plus RT at 6%, which means our R is equals to 0,06. And how long will it take Joseph's investment to grow to 55, which means our S is 55,404. Now, since we know what the formula looks like, we can then just substitute into the formula. S is equals to P times 1 plus RT. Our S is 55,440 is equals to our P is 36,000 times 1 plus our rate, which is 0,06. And our T is what we are looking for. Now, we need to make T the subject of the formula. To do that, it means there are a couple of things that we need to do. In order to get the rate of 36,000, we need to divide this side by 36,000. And also it means we must divide this side by 36,000. There, 36,000 and 36,000 will cancel out and you will be left with 1 plus 0,06. I'm just going to put T there because it's just a multiply by T. And on the other side, I have 55,440 divided by 36,000. I am left with 1.54 on the other side. Now, the next step is to get the rate of 1 from this side. So because it's positive, this side is going to be 0,6T and this side will be 1,54 minus 1, which is 0,54. And this side will be 0,06T. Now, we are only interested in having T on its own, so we divide this side by 0,06. Therefore, it means we divide this side by 0,06. What you do on the left, you must do on the right. T will be equal to 0,054 divided by 0,06 equals 9. The answer is 9, yes. See how easy it is to do some calculations. Any questions, any comments, any query, anything that is not clear that you want me to go over again. If not, then we move to the next question. But you guys, you need to unmute, you need to talk to me because after these two questions, I'm going to give you some time, like two minutes, five minutes, depending on the complexity of a question to do the question. And I want you to engage with me. I want you to talk to me. I want you to answer the question as well. So let's look at the last exercise where my voice will be heard. Me explaining certain things. Okay, so the question states, can the science and agreement to pay 20,000, 20,000, 15 months ago? The simple discount rate is 12,5 per annum. The discounted amount she receives now equals 15 months ago, they signed a contract of 20,000. They had a simple discount rate of 12.5% per annum. The discounted amount now she receives will be equals 12. So now we want to know what will be the discounted amount. I'm going to give you some few minutes to think about it. Then we go into answer the question. Have we now thought about the question? Okay, so let's identify what we are given. She signs the contract to pay 20,000. So this is our present value 15 months ago. This is our period T, which will be 15 divided by 12. And a simple discount rate. So this will be our deal. This is 12.5 divided by 100. That will be 0.125. And we are looking for the discounted amount, which is our DV amount. So we can use this formula or that formula. We can calculate the discount and then we can calculate the discounted amount. So let's use the second one. So DV is equals to P times 1 minus GT. Our present value is 20,000. 1 minus our D of 0 comma 125 times our period, which is 15 over 12. Because it has to be in years. Now let's calculate. I'm going to start with 15 divided by 12. It's 1.25 times 0.125. It's 0. Let me write it all out. That will be 20,000 times 1 minus 0.15625625. And if I take 1 minus 0.15625, I get 0.8457. Multiply that by 20,000. I get the amount of 16,875. And that is equals to option 4. Happiness. Are we good? And that is how you work out the questions. Now it's your turn. It's your turn. It's your time to answer some of the questions. Exercise 3. How much simple interest is payable on a loan of 40,000 Borot for a period of 22 months at a simple interest rate of 10%. Firstly, ask yourself, what are you giving in this question? Number two, identify the formula that you're going to be using. Read the question carefully because you don't have to complicate your life. How much interest, simple interest, so they're looking for, I'm just going to give you a hint. And I think that will be the last time I give hints. To get decimals on your financial calculator, press setup, and then press 0. You always need to have it to 4 decimals of your calculator, press 0. And then press 0 again. And then press how many digits you want. So let's say your calculator needs to always be on 4 decimals. Then you're going to press 4 for 4 decimals. But if you're answering questions because your calculator is on the mode in terms of 4 decimals, you just need to press setup, 0, 0, and 2, it will take your calculator to 2 decimals. Once you get your answer, go back to the setup, 0, 0, 4, and leave your calculator at 4 decimals. It's easy when you are doing some calculations. Right. Do we have an answer? I saw some answers on there saying option 2, option 2, option 2, 10. Are we all done? It should be the easiest calculation to do. Yes. Okay. How do we answer it? So first, let's identify what we are given. So what formula are we going to use? Let's start there first. What formula? I equals to P R T. R T. So if we know what formula, so what is our P? 40,000. I'm going to write it here. Our P is 40,000. What is our R? 10%. So our R will be 0, 1. You can say 1, 0 is still fine. And our T? 22 over 12. It will be 22 over 12. And we can then come here and substitute, right? Which will be 40,000 times our R of 0, 1 times 22 over 12. And the answer that you get is? 733.33. 1, 3, 3, 3.33. Money, we leave it to 2 decimals unless if your answer is whole number. So that's how you will answer that question. That is how much interest you would have paid. Any questions before I move? Anyone who was lost? Nobody. Okay. The next question, I'm going to also give you some two minutes to answer it. Here, I'm not even going to bother to tell you what formula, what, what. No, I want you to identify things and answer the question without my help. Read the question. Check what is given. Identify the formula after you read the question. Then state the facts. What is it that is given in the question? And substitute into that formula and calculate. So after I invested one half of his savings in a bond that paid 195, something interest for you for two years. So that was total savings before making the investment. Oh, same as well, back. Okay, okay, okay, okay. Time initial. All right. I have a question again. My calculator keeps on rounding the totals like when it's 9.5 divided by 100. It gives me 0.10. Your calculator, is it on two decimals or is it on four decimal? It's on two now. Should I change it to four? Yes, always change it to four. Once you answer the question, change it back to four decimal. Okay, I will do so. I have someone saying two, one. Someone says two, someone says one. I cannot get on the chat, but I also get one. And you also get one. Okay. Just that invested one and a half of his savings into the bond that paid 9.5 interest rates per annum for two years and received 589 rent as interest. What is the value of his total? I'm going to stress this. The value of his total savings before making an investment. So let's see if the answer is one or the answer is two. Okay. Let's see. Okay. So what are we looking for? We're looking for some sort of a total value. I'm going to call that a total value because I don't know what that is. It's not the value, it's not the present value, but that is the total value before making an investment because it takes part of that total value and make an investment of it. I hope you read the question like that as well. So just that invested one half of his savings. So what is one half? If I have two thousand, let's for argument sake, if I have two thousand, what will be one half of two thousand? One thousand. Is it one thousand? Yeah. So one half of this will be a thousand. Okay. So if I have, this is my total amount. If I take one half of it, it means I'm taking a thousand and investing it. That's what the question is asking you to do, to think, actually. So he invests one half of his total investment, which will help us answer that at some time. In a bond that pays 9.5 simple interest rate. So therefore, yeah, we can say we don't know what our P is because we don't know how much he is investing into this. We know that it's one half of the total investment that he has. Or savings. And this is our R. R will be 0.095, right? That's how you answered it. Because it's 9.5 divided by 100. So two years, that should be your T, right? And this is our interest, which is I. So therefore, it means we need to calculate or we need to find P, which is P is equals to one plus RT. That's what we are looking for. Or we don't even have to complicate our life. In this instance, we can just use P and RT in a way. And that will give us here, substituting the values, 589. P is what we are looking for. And we can divide the site by RT, divide the site by RT. I'm just going to divide the site by R, which is 0.095 times our T of two years. Therefore P is equals to the money that he is investing to get an interest of 589 is, what did you get? What is 589 divided by 0.92 times? What did you get? 3100. 3100. 3100. That is the amount that they deposited. So the total saving that they have, it was one half plus one half of that should give us how much he had. So we know one half is 3100. So it means one half is 3100 plus that. So we could have just said it's two times. Is that what you did? So which will be 3200. And the answer will be two. Any question? Any comment? So it means when you answer questions like this, always think outside the box. Sometimes it's not as straightforward as you might think. Sometimes they might even ask you when they double the amount or find the interest after the amount double, the investment doubles too. So you need to come up with those type of other fictitious amount that you can use to substitute in terms of what is a double. A double of 100 is 200. A double of a 3,000 is 6,000. Things like that. So even on this question, you just need to understand the words and interpret them in a way that you will make sense when you answer the question as well. Okay. Question five. Suppose you invest 10,000 at a simple interest rate of 12% per annum. What would be the value of the accumulated amount after six years? I'm also not going to assist you here. So you just need to answer. And then I will check on the check what you have. Okay. Seems like the answer here is fairly easy to calculate. So anyone who wants to answer the question, what are we given? What are we given? So we were given the P, the 10,000 is the P. Okay. It will be our P and then our R will be the 12%. So now they're asking for the future value of the accumulated amount, which is going to be our S that will be calculated. And then our T will be six. So we will basically use that formula that says S is equal to P into one plus RT. We will put in our values. It will be 10,000 into one plus 0.2, which is our 12% multiplied by six. Then we'll get our answer of 17,200, which is number four. Happiness? Yes. Next question. 3,450 ends a simple interest and accumulates to 5,623 and 50 cents after seven years. Had the yearly interest rate been 2% more, how much interest would he have accumulated in seven years? Are we winning? Are we there yet? I see number four, number one. So I'm not sure this, I'm thinking this number, what am I seeing? Number three, number four, number one, I'm not sure those number ones and number fours are part of the previous question. I will start checking the numbers from 657. So number three, number three. Let's see if that's what, if you are right. So let's read the question carefully. An amount of 3,450 ends a simple interest. And accumulates to 5,623 and 50 cents after seven years. So we are given near P, we are given near S, we are given near T. That's easy. What they haven't given us here is the rate, how much will be the rate, but we can always calculate here without even reading the questions even going further. We can always calculate and find out what would be the, what you call that thing now, the interest. Because if I calculate what interest is, interest is P minus, P minus I, sorry. What am I saying? Future value is P minus I. So I'm given the future value and I'm given this. So if I take this, I can say 500 and 57 minus. So I can also say it's I is equals to S minus P. It can still work the same and that will give me my interest. But that's not what we want. Because we need to read the question fully. Because the question says, had the yearly interest rate been more, 2% more? How much the interest he would have accumulated? So because I don't know. What the interest rate was then? Because I need to know what interest rate is. The simple interest rate. What was it so that I can increase it more and be able to get my interest? Oh, I can calculate my interest here and then multiply that with 2% more and see if that will give me my interest. Anyway, let's do what we are told to do. So the first thing that I would do is find the interest. So S is equals to P times 1 plus R. T will give us the interest because I'm given my future value, which is 5623.50. And if someone did it differently to mine, you can also say so that we, and if we get the same answer and our P, which is and our P, which is 3450 times 1 plus. We don't know what R is, but we do know what T is. T is 7. Now we need to remove the divide the side by 3450. Divide the side by 3450. What do we get on the other side? 5623.50 Divide by 3450. It's 1.63. And this side I was left with 1 plus 7R because 7 times R is just 7R. And I'm going to subtract this side 1.63 minus 1. And this side I'm left with 7R. And this side will be 0.63 equals to 7.7R. And divide the side by 7 and divide the side 0.63 divided by 7. Our rate, what is 0.63 divided by 7? Our rate is 0.09. So we know that our interest in this instance, if we take 5623.50, 0.50, subtract 3450, our interest here would have been, what would have it been? 5623.50, subtract 3450 equals our interest at 9% would have been 2173.50. That would be the interest. If that was the question asked interest. However, they say if the interest was 2% more, how much interest would we be? So it means we need to take the 0.9 and 2% more will be 0.02, which gives us the rate of 0.11. Isn't it? Right? Happiness, which will be 0.11, which is our rate. Now we can calculate how much interest. We can either take even, we can take this 0.2 and multiply it there and get the rate, but let's do it the old school way. The old school way will be, I is equals to what is our current or present value times the rate that is what we calculated just now, times the period that they told us for seven years. So we take 3450, multiply that with the rate of 0.11, multiply that with the term of seven years. And the answer that you get is, those with calculators, 3450 times 0.11 times 7 equals 2,600 and 56th range, 50 cents, which is option four. I don't know those who got 483. You could have took a hint in terms of the first one. You can see that 483 is lower than even the interest of the first one. Even though we didn't know what the interest is, but we can calculate what the interest would be. So if I take 2173.50 and I multiply that, I'm not sure, but I'm just gonna try. By two, I will still not get the right answer because it's not even going to give me. So you need to do it this way so that you can get the right answer. Okay. All right. All right. Any questions? Any comments? I have so many exercises, but the time is running out as well. So let's see if we can get to this one. Determine the amount that has been invested now to be worth 10,000 in eight months time if the annual simple interest rate is 9.75. So you need to determine what are you given. I'm gonna do that for you so that you save time to go to the next one. The question is asking us to determine the amount that has to be invested, which is our present value. That will be worth 10,000, which is a future value in eight months, which is the period of eight divided by 12. If the financial simple interest rate of R is equals to 0.0975 and you know the formula to use S is equals to P times 1 plus RT and because we calculate in P, we can always say the formula will be P is equals to S over. So let's take everything that is dividing here. We divide, we take everything in the bracket and divide S by it. So it will be 1 plus RT. You don't even have to put it in the bracket. You can just do it that way. And that's how you do changing the subject of the formula and substitute and answer the question. Are we happy? So I see the answer here. They say number two. The other person said four and then quickly changed it to number two. Okay. So it means you've got the answer. Let's do the calculation. Our S is 10,000, right? One plus our R, 0,0975. Five times our T of eight over 12. Are you still there? Oh, sorry. I am still here. Sorry. My bad. My bad. I am still here. I want to stop sharing and share again. Sorry. I was opening my calculator and doing some calculation. I forgot that you can see what I'm calculating. So there is the answer. The same way as I wrote it here. And the answer is 93867. 9389.67, which is option number two. Right. So let's move to the next one. Are they all simple interests? I just want to check. Yes, they are all simple interests. So Mr. Mangena invested an amount of 18,890, divided it into two schemes. Scheme A and Scheme B at a simple interest rate of 14% per annum and 11% per annum respectively. If the total amount of simple interest and in three years is 5,508, then what was the total amount invested in Scheme B? If the total amount invested in simple interest and in three years is 5,508, what was the total amount invested in Scheme B? Remember that Scheme B had 11%. Which is a little bit tricky with this one. Yes, it seems like it. However, because they didn't tell us if it was divided halfway like what do you call it? Equally. But they say it was divided into two different schemes. Scheme A and Scheme B, but remember now they are paid in different, like the end different interest. So you can calculate, you can take half of it and put it in Scheme A and half of it in Scheme B and see if the interest, the total interest comes to this. And if it comes to that, then you will know how much in Scheme B he invests, but that's what they want to know, how much they invested in Scheme A and Scheme B. Yeah. Okay. No, that is not as easy as I thought. So, alternatively, what we can do is do both at the same time. If we know that the S for one plus the S for the other one should give us the total. That's all what we know. So P of one plus RT plus P of one plus RT should give us the future value, the same future value for both. We know that we don't know what the P's are, but what we know is the R and the T. We know the total amount. We don't know the total amount, but we also know the P of that. So we know that interest of one plus interest of the other should give us the total interest. That's the other way of doing it. Yeah. However, we don't have the P's. So P RT plus P RT should give us the total, but we know what the total is. So the total is 5,508. We know that the P times our rate for one, let's say for P for one is 0,14, right? And the time, so the T for one, both of them are invested for three years, right? So that will be three plus P, and this one, which will be 0,11 times T of three years. So this will be 5,508 P times, or we can say it's 0, the challenge I also have now is that we know what the P is because that is our P. We substitute the P and find, because we know the P is 13,000. This will be 0,33. And this will be 0,14 times 3 is 0,42. 0,42P P, which is, if I take the P, then there will be 2P out. No, there will be 1P out. And this will be 0,42 plus 0,33. Oh, probably still gonna take me back to the same answer because then it will say 5,508 divided by into bracket 0,42 plus 0,33. 7,000. No, no, no, no, no, no. I will share this one on WhatsApp because I don't know the answer is yet. And it needs someone to think long and hard and we don't have that type to think long and hard. So number eight, we'll redo that. We'll share the, I'll share the solution on WhatsApp. What time is it now? And we have nine minutes. Okay, I will think about this one. Okay, but I am not on WhatsApp with you guys. Then you will have to ask, you can send an email once I have the answer. You can ask during the week if I have an answer with you. Yeah. Okay. So I have also some of the activities. I'm just gonna, for the recording. So you can go through them as well at your own time. You can take a picture as well. You can go and do this for how long 1,500 to be invested at 12% gaining an interest of 405. So you need to calculate your T, the other one. Yeah. They talk about discount rate, how much money they should receive and what size of the loan will that be. So it means you need to calculate two questions. The next one, invest 4,000 or 45,000 at simple interest and later on the 20,000. So you just need to take into consideration that the first one and later on the second one at the same interest rate determine the amount that Susan will have saved after three years. So one will be only for a year and the other one will be for the full three years because two years later they add 20,000. You need to calculate them separately and add them together afterwards. So 45,000 for three years, 20,000 only one year because it says two years later. So it's only after two years and they're only doing it for only three years. So 20,000 for only one year. T will be one. How much money must she invest? Okay, I think this one looks almost the same as the previous one must invest simple interest for three years and six months. So now remember to convert six months into the same. So this six months will be 0.5 because six divided by 12, it's five. So this will be 3.5 years. And if this was an accumulated, if the 5,250 interest is end, so this is the interest. So you need to calculate how much money must be invested, which is a P. Then the next one, six years ago, the boy invested 18,000 a yearly two years if he drew the amount. So 13,006 years. It accumulated interest and how much will it be? Two years ago, they withdrew. So two years ago, you will need to do the math now. They withdrew the total accumulated sum of 17,000 and the yearly simple interest rate at which table they were invested to the 13,006 years ago rounded to one decimal. So they just want to know what the simple interest is. So you just use that one. So the other information is just there to confuse you a little bit, but not really because yet they talk about cumulative amount as well. But you just need to calculate the simple interest. Okay, so as we come to the end of the session. So what we have done today, we looked at simple interest and simple discount and these are the formulas. You just need to remember that simple interest is just the amount you end if you save amount or the amount you pay when you borrow the money. And it's I is equals to PRT and the future value is calculated by S is equals to P times one plus RT and if they give you the future value and they ask you to find the present value, you can make P the subject of the formula to calculate the present value of the simple interest. Discount, you can calculate the discount which will be given by D is equals to your present value times the rate times the period and from there you can also calculate the discounted value which will be P times one minus RT and that's how you will calculate simple interest. The key words here is when you read questions always identify what the question is asking you in terms of because they will give you some key words like simple interest and that will give you an idea that you need to use the formula and remember simple interest and simple discount we only use formulas. Whether you have a financial calculator or you have a cashier or a shop calculator or an HP calculator, you always always use the formula. And that concludes our meeting for today. Are there any questions, comments, query? Can you put exercise eight quickly up? I just wanted to make a screenshot of it quickly. No problem. Otherwise, all the notes are uploaded. Let me just show you where to find all this. You don't even have to take a picture. You can go and get the notes for today. I'm just going to open one of this. I'm just going to go because there is no schedule for today but I'm just going to go to any of the so if on Monday or next week or anyway when you get the link to the session when you click on open class notes it should take you to the session that we have. For example, under the BNQMI basic numeruses it will take you to the folder. So you will have access to all these notes. Today's notes, today's the second, right? These are the notes that we use for today. So it's just the same presentation as I've gone through. So exercise eight, it will be there as well. It will be there as well as part of the notes plus the additional activities that I said you can go through as well. So these exercise eight and the others there are there. And that's it from me for today. I just need to go back to the presentation. Are there any other questions we left with one minute? So I'm confused. How do we get those notes again? I'm in here and I don't see them. Yeah, you won't see today's sessions because you can see that it starts on the second because today it's public holiday. UNICEF is not waking. So because we requested that we have the session for today. So Monday is a public holiday. So you don't get that. But hopefully by next week or something. Let me see if I can hack the system. I'm going to teach you how to hack the system. So we are on 243. I'm not sure where is the thing. I'm just going to take it. It's not 241. You can see that I'm not even sure where is the thing. So maybe it's 239. I always just check like that because I don't know which one is 238. No. 36, no. Okay. I don't know which module will that be. Yeah, 35. Otherwise that you're going to stay here forever and ever. It's not that. And there we go. So once you click on there, when you go to your browser and it says module number, you must write this down. Module 233, you just change the value there to 233. And there it is. And then you just click on open class notes. And then I'm teaching you how to hack the systems. So that's where you will find. And there are some recordings as well for the past exercises that we did. Those who are doing BNU. Remember the other session we had was with the statistics question. And I'm not seeing stats here. I was going to say you can go to the stats, but I'm not seeing that. So you just need to change your module number to 233 there at the top. And then it will take you to this folder structure. And then you just click here. It will take you to the same information that we have. Your view will be different to my view. You will only be seeing the notes. You won't be seeing all these other things because I'm the facilitator. I have access to the administrative side of things. So that's why I see so many things, but you will have the notes and the schedule of what we're going to be discussing the whole of May. Okay, right. That concludes today's session. Have a lovely evening. If there are no questions, I'm going to post again the register. I'm sure that you complete the register before you leave if you haven't done so. Otherwise, thank you for coming and sacrificing your public holiday with me.